Two new mathematical theories of complement activation were developed. One can be used to analyze data related to the final stages of complement activation; in particular percent hemolysis as a function of EAc1-8/C9 ratio. From this information, it is possible to obtain, in principle, the distribution of sizes of lytic holes. The other development is a method for analyzing steady state hemolysis, as a function of the time lag between Ig and complement addition. Preparation of cells with known epitope densities permits inferences to be drawn about the effects of valence, epitope density and distribution of Igs required for lysis.